How do I differentiate (e^(2x)+1)^3?

You might be tempted to start by expanding the brackets, but in this case it's much easier to use the chain rule. This is the rule that, to differentiate f(g(x)), we find f'(g(x))*g'(x). In other words, to differentiate a function of a function of x, we first differentiate the 'outside' function while leaving the 'inside' function unchanged; then we differentiate the 'inside' function; then we multiply the two together. In this case, the inside function (g) is the e^(2x)+1 and the outside function (f) is the 'cubed'. Therefore, f'(g(x)) = 3(e^(2x)+1)^2, and g'(x) = 2(e^(2x)). So:(d/dx)((e^(2x)+1)^3) = (3(e^(2x)+1)^2) * 2(e^(2x)) = 6((e^(2x)+1)^2)(e^(2x))

AH
Answered by Alfie H. Maths tutor

3807 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Find the total area enclosed between y = x^3 - x, the x axis and the lines x = 1 and x= -1 . (Why do i get 0 as an answer?)


Find the area bounded by the curve y=(sin(x))^2 and the x-axis, between the points x=0 and x=pi/2


Show that 2sin(2x)-3cos(2x)-3sin(x)+3=sin(x)(4cos(x)+6sin(x)-3)


Differentiate a^x


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

MyTutor is part of the IXL family of brands:

© 2025 by IXL Learning